Michael is $3$ times as old as Brandon. $18$ years ago, Michael was $9$ times as old as Brandon. How old is Brandon now?
Explanation: We can use the given information to write down two equations that describe the ages of Michael and Brandon. Let Michael's current age be $m$ and Brandon's current age be $b$. The information in the first sentence can be expressed in the following equation: ${m = 3b}$ Eighteen years ago, Michael was $m - 18$ years old, and Brandon was $b - 18$ years old. The information in the second sentence can be expressed in the following equation: ${m - 18 = 9(b - 18)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$, it might be easiest to use our first equation for $m$ and substitute it into our second equation. Our first equation is: ${m = 3b}$. Substituting this into our second equation, we get: ${3b} {-18 = 9(b - 18)}$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $3 b - 18 = 9 b - 162$. Solving for $b$, we get: $6 b = 144.$ $b = 24$.